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 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "<img align=\"left\" style=\"padding-right:10px;\" src=\"figures/PDSH-cover-small.png\">\n",
    "\n",
    "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
    "\n",
    "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [Feature Engineering](05.04-Feature-Engineering.ipynb) | [Contents](Index.ipynb) | [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.05-Naive-Bayes.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In Depth: Naive Bayes Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
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   "source": [
    "The previous four sections have given a general overview of the concepts of machine learning.\n",
    "In this section and the ones that follow, we will be taking a closer look at several specific algorithms for supervised and unsupervised learning, starting here with naive Bayes classification.\n",
    "\n",
    "Naive Bayes models are a group of extremely fast and simple classification algorithms that are often suitable for very high-dimensional datasets.\n",
    "Because they are so fast and have so few tunable parameters, they end up being very useful as a quick-and-dirty baseline for a classification problem.\n",
    "This section will focus on an intuitive explanation of how naive Bayes classifiers work, followed by a couple examples of them in action on some datasets."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Bayesian Classification\n",
    "\n",
    "Naive Bayes classifiers are built on Bayesian classification methods.\n",
    "These rely on Bayes's theorem, which is an equation describing the relationship of conditional probabilities of statistical quantities.\n",
    "In Bayesian classification, we're interested in finding the probability of a label given some observed features, which we can write as $P(L~|~{\\rm features})$.\n",
    "Bayes's theorem tells us how to express this in terms of quantities we can compute more directly:\n",
    "\n",
    "$$\n",
    "P(L~|~{\\rm features}) = \\frac{P({\\rm features}~|~L)P(L)}{P({\\rm features})}\n",
    "$$\n",
    "\n",
    "If we are trying to decide between two labels—let's call them $L_1$ and $L_2$—then one way to make this decision is to compute the ratio of the posterior probabilities for each label:\n",
    "\n",
    "$$\n",
    "\\frac{P(L_1~|~{\\rm features})}{P(L_2~|~{\\rm features})} = \\frac{P({\\rm features}~|~L_1)}{P({\\rm features}~|~L_2)}\\frac{P(L_1)}{P(L_2)}\n",
    "$$\n",
    "\n",
    "All we need now is some model by which we can compute $P({\\rm features}~|~L_i)$ for each label.\n",
    "Such a model is called a *generative model* because it specifies the hypothetical random process that generates the data.\n",
    "Specifying this generative model for each label is the main piece of the training of such a Bayesian classifier.\n",
    "The general version of such a training step is a very difficult task, but we can make it simpler through the use of some simplifying assumptions about the form of this model.\n",
    "\n",
    "This is where the \"naive\" in \"naive Bayes\" comes in: if we make very naive assumptions about the generative model for each label, we can find a rough approximation of the generative model for each class, and then proceed with the Bayesian classification.\n",
    "Different types of naive Bayes classifiers rest on different naive assumptions about the data, and we will examine a few of these in the following sections.\n",
    "\n",
    "We begin with the standard imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Gaussian Naive Bayes\n",
    "\n",
    "Perhaps the easiest naive Bayes classifier to understand is Gaussian naive Bayes.\n",
    "In this classifier, the assumption is that *data from each label is drawn from a simple Gaussian distribution*.\n",
    "Imagine that you have the following data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
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/EkTvg4do3DDjw71ffDSOMvMXs/PwGeLikyhTNJCX+nShdo3M660CvDpkAJHR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116167550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "X, y = make_blobs(100, 2, centers=2, random_state=2, cluster_std=1.5)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "One extremely fast way to create a simple model is to assume that the data is described by a Gaussian distribution with no covariance between dimensions.\n",
    "This model can be fit by simply finding the mean and standard deviation of the points within each label, which is all you need to define such a distribution.\n",
    "The result of this naive Gaussian assumption is shown in the following figure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "![(run code in Appendix to generate image)](figures/05.05-gaussian-NB.png)\n",
    "[figure source in Appendix](06.00-Figure-Code.ipynb#Gaussian-Naive-Bayes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "The ellipses here represent the Gaussian generative model for each label, with larger probability toward the center of the ellipses.\n",
    "With this generative model in place for each class, we have a simple recipe to compute the likelihood $P({\\rm features}~|~L_1)$ for any data point, and thus we can quickly compute the posterior ratio and determine which label is the most probable for a given point.\n",
    "\n",
    "This procedure is implemented in Scikit-Learn's ``sklearn.naive_bayes.GaussianNB`` estimator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "model = GaussianNB()\n",
    "model.fit(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's generate some new data and predict the label:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "Xnew = [-6, -14] + [14, 18] * rng.rand(2000, 2)\n",
    "ynew = model.predict(Xnew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now we can plot this new data to get an idea of where the decision boundary is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BStMIUMYwjB4md3HO7+lDPBafhHGWUvZphywrkJUNuGUO6lYRFEV5sL5MCAGB2cDLtDDE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hAAAg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\nqVV54uXPoVGvE3b6ub0dGb1kjdb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tFLpwYHT9F+kHKTLKGAwC0iihvrxIIAY0jRJhnJ/r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\nCiussMIKK1xnWAXnFVZYYYUVVrjO8P8DYfQSJAwZ8HAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118a16d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='RdBu')\n",
    "lim = plt.axis()\n",
    "plt.scatter(Xnew[:, 0], Xnew[:, 1], c=ynew, s=20, cmap='RdBu', alpha=0.1)\n",
    "plt.axis(lim);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We see a slightly curved boundary in the classifications—in general, the boundary in Gaussian naive Bayes is quadratic.\n",
    "\n",
    "A nice piece of this Bayesian formalism is that it naturally allows for probabilistic classification, which we can compute using the ``predict_proba`` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.89,  0.11],\n",
       "       [ 1.  ,  0.  ],\n",
       "       [ 1.  ,  0.  ],\n",
       "       [ 1.  ,  0.  ],\n",
       "       [ 1.  ,  0.  ],\n",
       "       [ 1.  ,  0.  ],\n",
       "       [ 0.  ,  1.  ],\n",
       "       [ 0.15,  0.85]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yprob = model.predict_proba(Xnew)\n",
    "yprob[-8:].round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The columns give the posterior probabilities of the first and second label, respectively.\n",
    "If you are looking for estimates of uncertainty in your classification, Bayesian approaches like this can be a useful approach.\n",
    "\n",
    "Of course, the final classification will only be as good as the model assumptions that lead to it, which is why Gaussian naive Bayes often does not produce very good results.\n",
    "Still, in many cases—especially as the number of features becomes large—this assumption is not detrimental enough to prevent Gaussian naive Bayes from being a useful method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Multinomial Naive Bayes\n",
    "\n",
    "The Gaussian assumption just described is by no means the only simple assumption that could be used to specify the generative distribution for each label.\n",
    "Another useful example is multinomial naive Bayes, where the features are assumed to be generated from a simple multinomial distribution.\n",
    "The multinomial distribution describes the probability of observing counts among a number of categories, and thus multinomial naive Bayes is most appropriate for features that represent counts or count rates.\n",
    "\n",
    "The idea is precisely the same as before, except that instead of modeling the data distribution with the best-fit Gaussian, we model the data distribuiton with a best-fit multinomial distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Example: Classifying Text\n",
    "\n",
    "One place where multinomial naive Bayes is often used is in text classification, where the features are related to word counts or frequencies within the documents to be classified.\n",
    "We discussed the extraction of such features from text in [Feature Engineering](05.04-Feature-Engineering.ipynb); here we will use the sparse word count features from the 20 Newsgroups corpus to show how we might classify these short documents into categories.\n",
    "\n",
    "Let's download the data and take a look at the target names:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['alt.atheism',\n",
       " 'comp.graphics',\n",
       " 'comp.os.ms-windows.misc',\n",
       " 'comp.sys.ibm.pc.hardware',\n",
       " 'comp.sys.mac.hardware',\n",
       " 'comp.windows.x',\n",
       " 'misc.forsale',\n",
       " 'rec.autos',\n",
       " 'rec.motorcycles',\n",
       " 'rec.sport.baseball',\n",
       " 'rec.sport.hockey',\n",
       " 'sci.crypt',\n",
       " 'sci.electronics',\n",
       " 'sci.med',\n",
       " 'sci.space',\n",
       " 'soc.religion.christian',\n",
       " 'talk.politics.guns',\n",
       " 'talk.politics.mideast',\n",
       " 'talk.politics.misc',\n",
       " 'talk.religion.misc']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_20newsgroups\n",
    "\n",
    "data = fetch_20newsgroups()\n",
    "data.target_names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "For simplicity here, we will select just a few of these categories, and download the training and testing set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "categories = ['talk.religion.misc', 'soc.religion.christian',\n",
    "              'sci.space', 'comp.graphics']\n",
    "train = fetch_20newsgroups(subset='train', categories=categories)\n",
    "test = fetch_20newsgroups(subset='test', categories=categories)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Here is a representative entry from the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From: dmcgee@uluhe.soest.hawaii.edu (Don McGee)\n",
      "Subject: Federal Hearing\n",
      "Originator: dmcgee@uluhe\n",
      "Organization: School of Ocean and Earth Science and Technology\n",
      "Distribution: usa\n",
      "Lines: 10\n",
      "\n",
      "\n",
      "Fact or rumor....?  Madalyn Murray O'Hare an atheist who eliminated the\n",
      "use of the bible reading and prayer in public schools 15 years ago is now\n",
      "going to appear before the FCC with a petition to stop the reading of the\n",
      "Gospel on the airways of America.  And she is also campaigning to remove\n",
      "Christmas programs, songs, etc from the public schools.  If it is true\n",
      "then mail to Federal Communications Commission 1919 H Street Washington DC\n",
      "20054 expressing your opposition to her request.  Reference Petition number\n",
      "\n",
      "2493.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(train.data[5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In order to use this data for machine learning, we need to be able to convert the content of each string into a vector of numbers.\n",
    "For this we will use the TF-IDF vectorizer (discussed in [Feature Engineering](05.04-Feature-Engineering.ipynb)), and create a pipeline that attaches it to a multinomial naive Bayes classifier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "from sklearn.naive_bayes import MultinomialNB\n",
    "from sklearn.pipeline import make_pipeline\n",
    "\n",
    "model = make_pipeline(TfidfVectorizer(), MultinomialNB())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "With this pipeline, we can apply the model to the training data, and predict labels for the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "model.fit(train.data, train.target)\n",
    "labels = model.predict(test.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now that we have predicted the labels for the test data, we can evaluate them to learn about the performance of the estimator.\n",
    "For example, here is the confusion matrix between the true and predicted labels for the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hXYsObNmyhccff5wFCxbQq1cvVqxYwaVLl4iPjyc2Npa9e/cCN765/F5CQgI+Pj7MnTuX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\nkBERkar9AwXLSNBV/8O+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118a3d1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "mat = confusion_matrix(test.target, labels)\n",
    "sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=False,\n",
    "            xticklabels=train.target_names, yticklabels=train.target_names)\n",
    "plt.xlabel('true label')\n",
    "plt.ylabel('predicted label');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Evidently, even this very simple classifier can successfully separate space talk from computer talk, but it gets confused between talk about religion and talk about Christianity.\n",
    "This is perhaps an expected area of confusion!\n",
    "\n",
    "The very cool thing here is that we now have the tools to determine the category for *any* string, using the ``predict()`` method of this pipeline.\n",
    "Here's a quick utility function that will return the prediction for a single string:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def predict_category(s, train=train, model=model):\n",
    "    pred = model.predict([s])\n",
    "    return train.target_names[pred[0]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's try it out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'sci.space'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict_category('sending a payload to the ISS')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'soc.religion.christian'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict_category('discussing islam vs atheism')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'comp.graphics'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict_category('determining the screen resolution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Remember that this is nothing more sophisticated than a simple probability model for the (weighted) frequency of each word in the string; nevertheless, the result is striking.\n",
    "Even a very naive algorithm, when used carefully and trained on a large set of high-dimensional data, can be surprisingly effective."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## When to Use Naive Bayes\n",
    "\n",
    "Because naive Bayesian classifiers make such stringent assumptions about data, they will generally not perform as well as a more complicated model.\n",
    "That said, they have several advantages:\n",
    "\n",
    "- They are extremely fast for both training and prediction\n",
    "- They provide straightforward probabilistic prediction\n",
    "- They are often very easily interpretable\n",
    "- They have very few (if any) tunable parameters\n",
    "\n",
    "These advantages mean a naive Bayesian classifier is often a good choice as an initial baseline classification.\n",
    "If it performs suitably, then congratulations: you have a very fast, very interpretable classifier for your problem.\n",
    "If it does not perform well, then you can begin exploring more sophisticated models, with some baseline knowledge of how well they should perform.\n",
    "\n",
    "Naive Bayes classifiers tend to perform especially well in one of the following situations:\n",
    "\n",
    "- When the naive assumptions actually match the data (very rare in practice)\n",
    "- For very well-separated categories, when model complexity is less important\n",
    "- For very high-dimensional data, when model complexity is less important\n",
    "\n",
    "The last two points seem distinct, but they actually are related: as the dimension of a dataset grows, it is much less likely for any two points to be found close together (after all, they must be close in *every single dimension* to be close overall).\n",
    "This means that clusters in high dimensions tend to be more separated, on average, than clusters in low dimensions, assuming the new dimensions actually add information.\n",
    "For this reason, simplistic classifiers like naive Bayes tend to work as well or better than more complicated classifiers as the dimensionality grows: once you have enough data, even a simple model can be very powerful."
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    "<!--NAVIGATION-->\n",
    "< [Feature Engineering](05.04-Feature-Engineering.ipynb) | [Contents](Index.ipynb) | [In Depth: Linear Regression](05.06-Linear-Regression.ipynb) >\n",
    "\n",
    "<a href=\"https://colab.research.google.com/github/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/05.05-Naive-Bayes.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n"
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